Question

Using the 32-bit binary representation for floating point numbers, represent the |

number 1011100110011_{2} as a 32 bit floating point
number. |

Answer #1

01000101101110011001100000000000Explanation: ------------- 1011100110011 => 1.011100110011 * 2^12 single precision: -------------------- sign bit is 0(+ve) exponent bits are (127+12=139) => 10001011 Divide 139 successively by 2 until the quotient is 0 > 139/2 = 69, remainder is 1 > 69/2 = 34, remainder is 1 > 34/2 = 17, remainder is 0 > 17/2 = 8, remainder is 1 > 8/2 = 4, remainder is 0 > 4/2 = 2, remainder is 0 > 2/2 = 1, remainder is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 10001011 So, 139 of decimal is 10001011 in binary frac/significant bits are 01110011001100000000000 so, 1011100110011_2 in single-precision format is 0 10001011 01110011001100000000000

Concern the following 16-bit floating point representation: The
first bit is the sign of the number (0 = +, 1 = -), the next nine
bits are the mantissa, the next bit is the sign of the exponent,
and the last five bits are the magnitude of the exponent. All
numbers are normalized, i.e. the first bit of the mantissa is one,
except for zero which is all zeros.
1. How many significant binary digits do numbers in this
representation...

Using the IEEE single-precision floating point representation,
find the decimal number represented by the following 32-bit
numbers, each expressed as an 8-digit hex number. Express your
answer using decimal scientific notation.
(a) (C6500000)16 (b) (31200000)16

If the IEEE Standard 754 representation of a floating point
number is given as 01101110110011010100000000000000, determine the
binary value represented by this 32-bit number

Matlab uses IEEE double precision numbers: 64-bit floating
point representation
1 bit : sign
11 bits: exponent
52 bits: mantissa.
Calculate largest number that can be stored
accurately
Calculate smallest number (x>0) that can be stored
accurately
Calculate the machine epsilon
Show all work step by step and explain
calculations
Now calculate the largest number and smallest number for a 10
bit floating point (1 bit for the sign, 4 bits exponent and 5 bits
mantissa)

Matlab uses IEEE double precision numbers: 64-bit floating point
representation
1 bit : sign
11 bits: exponent
52 bits: mantissa.
Calculate largest number (less than inf) that can be stored
accurately
Calculate smallest number (x>0) that can be stored
accurately
Calculate the machine epsilon
Show all work step by step and repeat for 10 bit floating point
(bit sign, 4 bits exponent and 5 bits mantissa)

Convert the following binary floating point number
100101.1001010101
using IEEE-756 single precision representation
Plz show work, thanks!

Given a 12-bit IEEE floating point format with 5 exponent
bits:
Give the hexadecimal representation for the bit-pattern
representing −∞−∞.
Give the hexadecimal representation for the bit-patterns
representing +0 and -1.
Give the decimal value for the floating point number represented
by the bit-pattern 0xcb0.
Give the decimal value for largest finite positive number which
can be represented?
Give the decimal value for the non-zero negative floating point
number having the smallest magnitude.
What are the smallest and largest magnitudes...

What is the 16-bit binary representation (in hexadecimal using
lower-case letters, e.g., 0x39ab) of -13 1/4 (base 10) when
represented as an IEEE 16-bit ﬂoating-point number? The IEEE 16-bit
ﬂoating-point representation uses formulae consistent with those
for the 32bit single-precision representation, except for using 5
bits for the exponent (instead of 8 in the case of the 32-bit
representation) and a bias of 15.

Represent the following decimal numbers using IEEE-754 floating
point representation. please show all work
i. -0.75
ii. 0
iii. - infinity
iv. 23
v. 10.25

How do you convert a decimal like 4.9219 into binary? (assuming
32-bit IEEE 754 floating point format)

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